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We describe a method to construct directed networks from multivariate timeseries which has several advantages over the widely accepted methods. Thismethod is based on an information theoretic reduction of linear(auto-regressive) models. The models are called reduced auto-regressive (RAR)models. The procedure of the proposed method is composed of three steps: (i)each time series is treated as a basic node of a network, (ii) multivariate RARmodels are built and the constituent information in the models is summarized,and (iii) nodes are connected with a directed link based on that summaryinformation. The proposed method is demonstrated for numerical data generatedby known systems, and applied to several actual time series of specialinterest. Although the proposed method can identify connectivity, there arethree points to keep in mind: (1) the proposed method cannot always identifynonlinear relationships among components, (2) as constructing RAR models isNP-hard, the network constructed by the proposed method might be near-optimalnetwork when we cannot perform an exhaustive search, and (3) it is difficult toconstruct appropriate networks when the observational noise is large.

Constructing directed networks from multivariate time series using linear modelling technique